Cryptology ePrint Archive: Report 2008/032

Merkle Puzzles are Optimal

Boaz Barak, Mohammad Mahmoody-Ghidary

Abstract: We prove that every key exchange protocol in the random oracle model in which the honest users make at most n queries to the oracle can be broken by an adversary making O(n^2) queries to the oracle. This improves on the previous Omega(n^6) query attack given by Impagliazzo and Rudich (STOC '89). Our bound is optimal up to a constant factor since Merkle (CACM '78) gave an n query key exchange protocol in this model that cannot be broken by an adversary making o(n^2) queries.